Same denominator
Same numerator.
Using number line, benchmarks fractions, justify with a model.
Begin with visual representations
Fractions with the same denominators
5 of one thing is more than 3 of the same thing.
Compare on number line.
Grid model.
Common numerators
Unit fractions - reasoning about denominators.
3 copies of a larger unit is more than the 3 copies of a smaller unit.
Tape diagrams
Think about sharing
Fraction towers
Relate numerators to denominators
Less than or greater than 1
Close to 0 or 1
Use benchmarks to compare
More or less than 1/2
Assume the same whole when comparing
Does each fraction refer to the same whole? Would you rather have 1/2 of a candy bar or 1/4 of a candy bar?
Potential difficulties with improper fractions
Be sure to define the whole
Number line is helpful - less confusing than area model
Potential comparison problems with self-constructed models
inaccurate sketches - might be better to use pre-drawn models
Misconceptions about comparison based on separately examining numerators
a/b > c/d if a>c and b>d NO!....3/8 < 1/2 9/10 >4/5
Looking at difference between numerator and denominator
Density of fractions
Comparing in K-5
2.MD.3
3.NF.3d
4.NF.2
Comparing in 6-8
6th Grade
Inequalities - 6.EE.8
7th Grade
Statistics and Probability - 7.SP.5
8th Grade
Irrational Numbers - 8.NS.2
Suggested Activities
Good questions in Uncomplicating Book
Suggestions for teaching
Number line - string across room. Give students index cards with different numbers on then. Let them clip to number line in the appropriate spot. There is a commercial version of this. Ask Sheila.
NCTM Illuminations - Fun with Fractions, comparing with set, area, and length models
Table of Contents
Comparing Strategies
Same denominatorSame numerator.
Using number line, benchmarks fractions, justify with a model.
Begin with visual representations
Fractions with the same denominators
- 5 of one thing is more than 3 of the same thing.
- Compare on number line.
- Grid model.
Common numerators- Unit fractions - reasoning about denominators.
- 3 copies of a larger unit is more than the 3 copies of a smaller unit.
- Tape diagrams
- Think about sharing
- Fraction towers
Relate numerators to denominators- Less than or greater than 1
- Close to 0 or 1
Use benchmarks to compare- More or less than 1/2
Assume the same whole when comparing- Does each fraction refer to the same whole? Would you rather have 1/2 of a candy bar or 1/4 of a candy bar?
Potential difficulties with improper fractions- Be sure to define the whole
- Number line is helpful - less confusing than area model
Potential comparison problems with self-constructed models- inaccurate sketches - might be better to use pre-drawn models
Misconceptions about comparison based on separately examining numerators- a/b > c/d if a>c and b>d NO!....3/8 < 1/2 9/10 >4/5
- Looking at difference between numerator and denominator
Density of fractionsComparing in K-5
Comparing in 6-8
6th Grade
- Inequalities - 6.EE.8
7th Grade- Statistics and Probability - 7.SP.5
8th GradeSuggested Activities
Good questions in Uncomplicating Book
Suggestions for teaching
Number line - string across room. Give students index cards with different numbers on then. Let them clip to number line in the appropriate spot. There is a commercial version of this. Ask Sheila.
NCTM Illuminations - Fun with Fractions, comparing with set, area, and length models